LC resonance, Q factor & bandwidth worksheet with answers

Free printable LC resonance, Q factor & bandwidth worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
C = 1 µF+−10 VL = 10 µHiL​

A 1 µF capacitor charged to 10 V is switched across an ideal 10 µH inductor. Find the peak current Imax in the circuit, in mA.

C = 1 µFV0 = 10 VL = 10 µH
Imax = mA
2.Easy
f|I|0.70712 kHzf1​f2​BW = 166.7 Hz

A resonance curve peaks at 2 kHz, and its half-power points are 166.7 Hz apart. Find the quality factor Q.

f0 = 2 kHzBW = 166.7 Hz
Q =
3.Medium
f|I|0.70712 kHzf1​ = ?f2​BW

A series RLC circuit resonates at 2 kHz with Q = 3. Find the lower half-power frequency f1 exactly, in kHz.

f0 = 2 kHzQ = 3
f1 = kHz
4.Medium
V5 Ω47 µH1 nF

A series RLC circuit has R = 5 Ω, L = 47 µH and C = 1 nF. Find its bandwidth BW in kHz.

R = 5 ΩL = 47 µHC = 1 nF
BW = kHz
5.Hard
C = 470 nFR = 1 ΩL = 22 mH

A charged 470 nF capacitor discharges through a 22 mH coil with a total series resistance of 1 Ω, so the oscillation slowly dies out. Its amplitude decays as e−Rt/(2L). How many oscillation cycles n pass before the amplitude has halved? (The losses are small, so the frequency is f₀.)

L = 22 mHC = 470 nFR = 1 Ω
n =
6.Hard
V2 Ω10 mH100 nF20 mA

A series RLC circuit (R = 2 Ω, L = 10 mH, C = 100 nF) is driven at resonance with a current amplitude of 20 mA. Find the energy Ecycle dissipated in R during one cycle, in nJ.

R = 2 ΩL = 10 mHC = 100 nFIm = 20 mA
Ecycle = nJ

Answer key

  1. 1. Imax = 3162 mA
  2. 2. Q = 12
  3. 3. f1 = 1.694 kHz
  4. 4. BW = 16.93 kHz
  5. 5. n = 47.74
  6. 6. Ecycle = 79.48 nJ

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